caa a22 4500 477076785 CHVBK 20180405111440.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF00047396 doi (NATIONALLICENCE)springer-10.1007/BF00047396 Koelink H. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001, Leuven (Heverlee), Belgium aut Askey-Wilson polynomials and the quantum SU(2) group: Survey and applications [Elektronische Daten] [H. Koelink] Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to Lie algebra like elements of the quantised universal enveloping algebra of sl(2). A full proof of the theorem announced by Noumi and Mimachi [Proc. Japan Acad. Sci. Ser. A 66 (1990), 146-149] describing the generalised matrix elements in terms of the full four-parameter family of Askey-Wilson polynomials is given. Various known and new applications of this interpretation are presented. Kluwer Academic Publishers, 1996 quantum group nationallicence SU(2) nationallicence Askey-Wilson polynomials nationallicence representation theory nationallicence matrix elements nationallicence dual q -Krawtchouk polynomials nationallicence spherical and associated spherical elements nationallicence continuous q -ultraspherical polynomials nationallicence q -Hahn polynomials nationallicence characters nationallicence Chebyshev polynomials nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers; http://www.wkap.nl 44/3(1996-09-01), 295-352 0167-8019 44:3<295 1996 44 10440 https://doi.org/10.1007/BF00047396 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00047396 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Koelink H. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001, Leuven (Heverlee), Belgium aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers; http://www.wkap.nl 44/3(1996-09-01), 295-352 0167-8019 44:3<295 1996 44 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer